Perspectives in Mathematical Sciences III

A dinosaur
LecturerNobuo YOSHIDA, Professor
DepartmentGraduate School of Mathematics, 2016 Spring
Recommended for:School of Science 4th year students (2週1回全15回)
Tags
  • mathematics
  • percolation
  • english
  • The Purpose of the Course

    This course is designed as one of the English courses which the Graduate School of Mathematics provides for the graduate and undergraduate students not only from foreign countries, but also domestic students who wish to study abroad or to communicate with foreign scientists in English. All course activities, including lectures, homework assignments, questions and consultations are in English. The purpose of this course is to introduce and explain various methods in mathematical sciences. This year, the course is organized by three instructors with different coverage of subjects from a variety of fields in mathematics.

    The Plan of the Course

    The course is divided into three parts (Part 1 by Yamagami, Part 2 by Yoshida and Part 3 by Ito) and the detail of part division will be announced at the first lecture time of the course. See the part syllabus provided by each instructor for more information.

    Keywords

    See the syllabus of each instructor.

    Required Knowledge

    Working knowledge of basic undergraduate mathematics, including calculus and linear algebra, is required.

    References

    See the syllabus of each instructor.

    Attendance

    This course is open for all students at Nagoya University as one of the "open subject" of general education.

    Additional Advice

    See the syllabus of each instructor.

    Part 2: Introduction to Percolation

    References

    [1] Grimmett, G. : "Percolation", Springer Verlag, 2nd Ed. (1999).

    [2] Higuchi, Y.: "Percolation" (In Japanese) Yuu-sei-sha, 2nd Ed. (2011)

    The Purpose of the Course

    The purpose of this course is to provide an introduction to the theory of percolation

    The Plan of the Course

    Here is a tentative outline:

    1. Percolation and random variable.

    2. The critical probability.

    3. The infinite cluster.

    Keywords

    d-dimensional integer lattice, percolation, critical probability, infinite cluster [Required Knowledge] basic notion in modern probability theory such as probability space, random variables and their independence.

    Attendance

    This course is open for all students of Nagoya University

    Additional Advice

    The reference [2] is easy to read. My office hours are Thursday 14:30 - 15:30.

    Lecture Handout

    The Method of Evaluation

    Three instructors evaluate their own parts independently in the order S,A,B,C,F,N(=Non-attendance) (see the part-wise course designs for further information) and the final grade of the couse is set to be the middle of these three scores (for example, if you get A,C,F as part scores, the course grade is set to be C).


    Last updated

    May 10, 2020